Basic graph counting sequences

[David Wilson]

Well, it turns out my two sequences are

    S = (1,1,2,4,11,...) = A000088
    T = (1,1,1,2,6,...) = A001349

(thanks to Eric W.) So I have discovered nothing new.

I will note that we should add an initial a(0) = 1 to A002494 and its 
b-file. Then

A000088 = partial sums of A002494
A001349 = inverse Euler transform of A000088
A000719 = A000088 - A001349

permits us to use the A002494 b-file to generate b-files for these 
sequences up to a(75).

These sequences could also be used as a basis for computing sequences

    G_k = n-node graphs having k connected components

for a few small k.